We study electric, thermal, and thermoelectric conductivities in the vicinity of a $z=2$ superconductor-diffusive metal transition in two dimensions, both in the high- and low-frequency limits. We find violation of the Wiedemann-Franz law and a dc thermoelectric conductivity α that does not vanish at low temperatures, in contrast to Fermi liquids. We introduce a Langevin equation formalism to study critical dynamics over a broad region surrounding the quantum critical point.
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Podolsky et al. (2007) studied this question.
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